scholarly journals Clause-Learning Algorithms with Many Restarts and Bounded-Width Resolution

2011 ◽  
Vol 40 ◽  
pp. 353-373 ◽  
Author(s):  
A. Atserias ◽  
J. K. Fichte ◽  
M. Thurley
Keyword(s):  
High Probability ◽  
Learning Algorithms ◽  
Sat Solvers ◽  
Unit Clause ◽  
Resolution Rule ◽  
Clause Learning ◽  
Bounded Width ◽  
Unit Resolution ◽  
Surprising Fact ◽  
Do So

We offer a new understanding of some aspects of practical SAT-solvers that are based on DPLL with unit-clause propagation, clause-learning, and restarts. We do so by analyzing a concrete algorithm which we claim is faithful to what practical solvers do. In particular, before making any new decision or restart, the solver repeatedly applies the unit-resolution rule until saturation, and leaves no component to the mercy of non-determinism except for some internal randomness. We prove the perhaps surprising fact that, although the solver is not explicitly designed for it, with high probability it ends up behaving as width-k resolution after no more than O(n^{2k+2}) conflicts and restarts, where n is the number of variables. In other words, width-k resolution can be thought of as O(n^{2k+2}) restarts of the unit-resolution rule with learning.

scholarly journals Clause-Learning Algorithms with Many Restarts and Bounded-Width Resolution

2009 ◽  
pp. 114-127 ◽  
Author(s):  
Albert Atserias ◽  
Johannes Klaus Fichte ◽  
Marc Thurley
Keyword(s):  
Learning Algorithms ◽  
Clause Learning ◽  
Bounded Width

scholarly journals Local Consistency and SAT-Solvers

2012 ◽  
Vol 43 ◽  
pp. 329-351 ◽  
Author(s):  
P. Jeavons ◽  
J. Petke
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Inference Rule ◽  
Constraint Satisfaction Problem ◽  
Constraint Satisfaction Problems ◽  
Fixed Size ◽  
Local Consistency ◽  
Sat Solvers ◽  
Clause Learning ◽  
Do So

Local consistency techniques such as k-consistency are a key component of specialised solvers for constraint satisfaction problems. In this paper we show that the power of using k-consistency techniques on a constraint satisfaction problem is precisely captured by using a particular inference rule, which we call negative-hyper-resolution, on the standard direct encoding of the problem into Boolean clauses. We also show that current clause-learning SAT-solvers will discover in expected polynomial time any inconsistency that can be deduced from a given set of clauses using negative-hyper-resolvents of a fixed size. We combine these two results to show that, without being explicitly designed to do so, current clause-learning SAT-solvers efficiently simulate k-consistency techniques, for all fixed values of k. We then give some experimental results to show that this feature allows clause-learning SAT-solvers to efficiently solve certain families of constraint problems which are challenging for conventional constraint-programming solvers.

scholarly journals Analysis of comparative effectiveness of state-of-the-art heuristics for CDCL SAT solvers

2021 ◽  
Author(s):  
S. Kochemazov
Keyword(s):  
Comparative Effectiveness ◽  
Major Part ◽  
State Of The Art ◽  
Learning Algorithms ◽  
Boolean Satisfiability ◽  
Satisfiability Problem ◽  
Sat Solvers ◽  
Boolean Satisfiability Problem ◽  
Clause Learning ◽  
Good For

The Conflict-Driven Clause Learning algorithms for solving the Boolean satisfiability problem comprise the major part of the methods used to solve various instances of the problems that arise in industry and science. In recent years there have been proposed several major heuristics for these algorithms which are assumed to be de facto good for the solvers’ performance over diverse sets of benchmarks. The goal of this paper is to evaluate the contribution of each separate heuristic to the performance of a state-of-the-art solver, see the extent to which they are beneficial, and figure out if the heuristics have any particular features that need to be taken into account.

scholarly journals Seeking Practical CDCL Insights from Theoretical SAT Benchmarks

2018 ◽  
Author(s):  
Jan Elffers ◽  
Jesús Giráldez-Cru ◽  
Stephan Gocht ◽  
Jakob Nordström ◽  
Laurent Simon
Keyword(s):  
Systematic Study ◽  
Boolean Satisfiability ◽  
Proof System ◽  
Sat Solvers ◽  
Proof Search ◽  
Wide Range ◽  
Clause Learning ◽  
Resolution Proof ◽  
Shed Light

Over the last decades Boolean satisfiability (SAT) solvers based on conflict-driven clause learning (CDCL) have developed to the point where they can handle formulas with millions of variables. Yet a deeper understanding of how these solvers can be so successful has remained elusive. In this work we shed light on CDCL performance by using theoretical benchmarks, which have the attractive features of being a) scalable, b) extremal with respect to different proof search parameters, and c) theoretically easy in the sense of having short proofs in the resolution proof system underlying CDCL. This allows for a systematic study of solver heuristics and how efficiently they search for proofs. We report results from extensive experiments on a wide range of benchmarks. Our findings include several examples where theory predicts and explains CDCL behaviour, but also raise a number of intriguing questions for further study.

Chapter 3. Complete Algorithms

2021 ◽  
Author(s):  
Adnan Darwiche ◽  
Knot Pipatsrisawat
Keyword(s):  
Real World ◽  
Theoretical Perspective ◽  
Point Of View ◽  
Sat Solving ◽  
Practical Point ◽  
Sat Solvers ◽  
Proof Systems ◽  
Real World Applications ◽  
Clause Learning

Complete SAT algorithms form an important part of the SAT literature. From a theoretical perspective, complete algorithms can be used as tools for studying the complexities of different proof systems. From a practical point of view, these algorithms form the basis for tackling SAT problems arising from real-world applications. The practicality of modern, complete SAT solvers undoubtedly contributes to the growing interest in the class of complete SAT algorithms. We review these algorithms in this chapter, including Davis-Putnum resolution, Stalmarck’s algorithm, symbolic SAT solving, the DPLL algorithm, and modern clause-learning SAT solvers. We also discuss the issue of certifying the answers of modern complete SAT solvers.

scholarly journals An Adaptive Strategy for Tuning Duplicate Trails in SAT Solvers

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 197
Author(s):  
Wenjing Chang ◽  
Yang Xu ◽  
Shuwei Chen
Keyword(s):  
Adaptive Strategy ◽  
Empirical Results ◽  
Sat Solvers ◽  
Decision Variables ◽  
Before And After ◽  
New Strategy ◽  
Clause Learning ◽  
Restart Strategy

In mainstream conflict driven clause learning (CDCL) solvers, because of frequent restarts and phase saving, there exists a large proportion of duplicate assignment trails before and after restarts, resulting in unnecessary time wastage during solving. This paper proposes a new strategy—identifying those duplicate assignments trails and dealing with them by changing the sort order. This approach’s performance is compared with that of the Luby static restart scheme and a dynamic Glucose-restart strategy. We show that the number of solved instances is increased by 3.2% and 4.6%. We also make a compassion with the MapleCOMSPS solver by testing against application benchmarks from the SAT Competitions 2015 to 2017. These empirical results provide further evidence of the benefits of the proposed heuristic, having the advantage of managing duplicate assignments trails and choosing appropriate decision variables adaptively.

scholarly journals Changes in the Rhythm of Speech Difference between People with Nondegenerative Mild Cognitive Impairment and with Preclinical Dementia

2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Juan J. G. Meilán ◽  
Francisco Martínez-Sánchez ◽  
Israel Martínez-Nicolás ◽  
Thide E. Llorente ◽  
Juan Carro
Keyword(s):  
Alzheimer’S Disease ◽  
Cognitive Impairment ◽  
Mild Cognitive Impairment ◽  
Older People ◽  
Lexical Access ◽  
High Probability ◽  
Its Analysis ◽  
Neurodegenerative Process ◽  
Speech Patterns ◽  
Do So

This study explores several speech parameters related to mild cognitive impairment, as well as those that might be flagging the presence of an underlying neurodegenerative process. Speech is an excellent biomarker because it is not invasive and, what is more, its analysis is rapid and economical. Our aim has been to ascertain whether the typical speech patterns of people with Alzheimer’s disease are also present during the disorder’s preclinical stages. To do so, we shall be using a task that involves reading out aloud. This is followed by an analysis of the recordings, looking for the possible parameters differentiating between those older people with MCI and a high probability of developing dementia and those with MCI that will not do so. We found that the disease’s most differentiating parameters prior to its onset involve changes in speech duration and an alteration in rhythm rate and intensity. These parameters seem to be related to the first difficulties in lexical access among older people with AD.

scholarly journals A Review on Various Algorithms used in Machine Learning

2019 ◽  
pp. 915-920
Author(s):  
Divya Chaudhary ◽  
Er. Richa Vasuja
Keyword(s):  
Machine Learning ◽  
Data Mining ◽  
New Technologies ◽  
Learning Algorithms ◽  
Machine Learning Algorithms ◽  
Learning System ◽  
Training Set ◽  
Learning Data ◽  
Do So

In today's scenario all of data is being generated by everyone of us . so it becomes vital for us to handle this data. To do so new technologies are being developed such as machine learning, data mining etc. This paper gives the study related to machine learning(ML).Precise approximations are repetitively being produced by Machine Learning algorithms. Machine learning system effectively “learns” how to guess from training set of completed jobs. The main purpose of the review is to give a jagged estimate or overview about the mostly used algorithms in machine learning.

scholarly journals FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraints

2020 ◽  
Vol 34 (02) ◽  
pp. 1552-1560
Author(s):  
Anastasios Kyrillidis ◽  
Anshumali Shrivastava ◽  
Moshe Vardi ◽  
Zhiwei Zhang
Keyword(s):  
Boolean Functions ◽  
Continuous Optimization ◽  
Conjunctive Normal Form ◽  
Cardinality Constraints ◽  
Sat Solvers ◽  
Boolean Satisfiability Problem ◽  
Algebraic Framework ◽  
Clause Learning ◽  
Sat Solver ◽  
Analysis Of Boolean Functions

The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side—especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT solvers—has been remarkable. Yet, while SAT solvers, aimed at solving industrial-scale benchmarks in Conjunctive Normal Form (CNF), have become quite mature, SAT solvers that are effective on other types of constraints (e.g., cardinality constraints and XORs) are less well-studied; a general approach to handling non-CNF constraints is still lacking. In addition, previous work indicated that for specific classes of benchmarks, the running time of extant SAT solvers depends heavily on properties of the formula and details of encoding, instead of the scale of the benchmarks, which adds uncertainty to expectations of running time.To address the issues above, we design FourierSAT, an incomplete SAT solver based on Fourier analysis of Boolean functions, a technique to represent Boolean functions by multilinear polynomials. By such a reduction to continuous optimization, we propose an algebraic framework for solving systems consisting of different types of constraints. The idea is to leverage gradient information to guide the search process in the direction of local improvements. Empirical results demonstrate that FourierSAT is more robust than other solvers on certain classes of benchmarks.

scholarly journals Post Mortem Analysis of SAT Solver Proofs

10.29007/gpp8 ◽  
2018 ◽  
Author(s):  
Laurent Simon
Keyword(s):  
Complex Systems ◽  
Learning Algorithms ◽  
Point Of View ◽  
Post Mortem ◽  
Learning Mechanism ◽  
Clause Learning ◽  
Sat Solver ◽  
Resolution Proofs ◽  
Final Proof

Conflict-Driven Clause Learning algorithms are well known from an engineerpoint of view. Thanks to Minisat, their designs are well understood, and mostof their implementations follow the same ideas, with essentially the samecomponents. Same heuristics, fast restarts, same learning mechanism.However, their efficiency has an important drawback: they are more and morelike complex systems and harder and harder to handle. Unfortunately, only afew works are focusing on understanding them rather than improving them. Inmost of the cases, their studies are often based on a generate and testpattern: An idea is added to an existing solver and if it improves itsefficiency the idea is published and kept. In this paper, we analyse``post-mortem'' the proofs given by one typical CDCL solver,Glucose. The originality of our approach is that we only consider it as aresolution proofs builder, and then we analyze some of the proofcharacteristics on a set of selected unsatisfiable instances, by shuffling each ofthem 200 times. We particularly focus on trying to characterize useless anduseful clauses in the proof as well as proofs shapes. We also show thatdespite their incredible efficiency, roughly 90% of the time spent in aCDCL is useless for producing the final proof.

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